Equations and Inequalities Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be either less than or equal to the value on the right.

Front

How do you solve the equation 5x - 7 = 8?

Back

To solve for x, add 7 to both sides to get 5x = 15, then divide by 5 to find x = 3.

Front

What is the first step in solving the inequality 50x + 400 ≤ 1,600?

Back

The first step is to subtract 400 from both sides, resulting in 50x ≤ 1,200.

Front

What is the hourly rate if a phone company charges a sign-up fee of $3.50 and Brian paid $75.50 for 12 hours?

Back

The equation to find the hourly rate x is 3.50 + 12x = 75.50.

Front

What does the solution x = 4 represent in an equation?

Back

It represents the value of x that makes the equation true when substituted back into the equation.

Front

Back

First, solve for x to get x > 32. Then, graph a number line with an open circle at 32 and shade to the right.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater or less than another.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be either greater than or equal to the value on the right.

Front

What is the solution to the equation 3x + 5 = 20?

Back

To solve for x, subtract 5 from both sides to get 3x = 15, then divide by 3 to find x = 5.